Conditional Expectations and Fock Space Representations in Quantum Filtering

The role on conditional expectations on von Neumann algebras in the theory of quantum filtering is investigated. The relations characterising the solutions of various quantum filtering problems are interpreted via the notion of conditional expectation. The equations that describe optimal linear quantum filters are represented in Fock space of the analytical functions, and the usefulness of this representation is discussed. Finally some priliminary results on the applications of these methods in non-linear and continous time filtering are described.